Abstract
Projection methods are a standard approach for the numerical solution of differential equations on manifolds. It is known that geometric properties (such as symplecticity or reversibility) are usually destroyed by such a discretization, even when the basic method is symplectic or symmetric. In this article, we introduce a new kind of projection methods, which allows us to recover the time-reversibility, an important property for long-time integrations.
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Hairer, E. Symmetric Projection Methods for Differential Equations on Manifolds. BIT Numerical Mathematics 40, 726–734 (2000). https://doi.org/10.1023/A:1022344502818
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DOI: https://doi.org/10.1023/A:1022344502818